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1.
Spectral pictures of Aluthge transforms of operators   总被引:4,自引:0,他引:4  
In this paper we continue our study, begun in [12], of the relationships between an arbitrary operatorT on Hilbert space and its Aluthge transform . In particular, we show that in most cases the spectral picture ofT coincides with that of , and we obtain some interesting connections betweenT and as a consequence.  相似文献   

2.
For an algebra of subsets of a set X there is constructed a set and an algebra of its subsets so that the mapping is a one-to-one correspondence between and and for each additive measure on the measure on defined by the equation is countably additive.Translated from Matematicheskie Zametki, Vol. 3, No. 1, pp. 71–76, January, 1968.The author wishes to express his deep appreciation to S. V. Fomin, under whose guidance this paper was written.  相似文献   

3.
Let be a Hilbert space. A continuous positive operatorT on uniquely determines a Hilbert space which is continuously imbedded in and for which with the canonical imbedding . A Kreîn space version of this result, however, is not valid in general. This paper provides a necessary and sufficient condition for that a continuous selfadjoint operatorT uniquely determines a Kreîn space ( ) which is continuously imbedded in and for which with the canonical imbedding .  相似文献   

4.
LetT be a contraction acting in a separable Hilbert space and leaving invariant a nest of subspaces of . We answer the question: when doesT have an isometric extension to which leaves invariant the nest = {N N :N ;}.  相似文献   

5.
Let M, resp. , denote Riemannian manifolds of dimensions m>4, resp. =m+2, and of constant sectional curvatures C, resp. , with 0 and is a standard space form, then the foliation L is a (globally) trivial fibre bundle with fibre Sm–1.  相似文献   

6.
Suppose is a von Neumann algebra on a Hilbert space and is any ideal in . We determine a topology on , for which the members of that are to norm continuous are exactly those in ; and a bornology on such that the elements of which map the unit ball to an element of , equivalently those members of that are norm to bounded, are exactly those in . This is achieved via analogues of the notions of injectivity and surjectivity in the theory of operator ideals on Banach spaces.  相似文献   

7.
Summary In this paper we treat a time-symmetrical Martin boundary theory for continuous parameter Markov chains. This is done by reversing the time sense of a Markov chainX t in such a way as to obtain a dual Markov chain , and considering the two chains together. Various relations between the Martin exit boundaries and of these processes are studied. The exit boundary of , is in a sense an entrance boundary forX t and vice versa. After a natural identification of certain points in and one can topologizeI in such a way thatboth X t and have standard modifications in this space which are right continuous, have left limits, and are strongly Markov.Research supported in part at Stanford University, Stanford, California under AFOSR 0049.  相似文献   

8.
Let denote an annulus,E a finite subset of with at least three elements, and the ideal of functions in which vanish at the points ofE. The quotient does not have a completely isometric representation on a finite dimensional Hilbert space. This complements a result of [11] which implies that the quotient has an isometric representation on a Hilbert space of dimension twice the cardinality ofE.  相似文献   

9.
Let be the unit disk in, be the Bergman space, consisting of all analytic functions from , and be the Bergman projection of onto . We constructC *-algebras , for functions of which the commutator of Toeplitz operators [T a ,T b ]=T a T b –T b T a is compact, and, at the same time, the semi-commutator [T a ,T b )=T a T b –T ab is not compact.It is proved, that for each finite set =n 0,n 1, ...,n m , where 1=n 0 1 <... m , andn k {}, there are algebras of the above type, such that the symbol algebras Sym of Toeplitz operator algebras arecommutative, while the symbol algebras Sym of the algebras , generated by multiplication operators and , haveirreducible representations exactly of dimensions n 0,n 1,..., n m .This work was partially supported by CONACYT Project 3114P-E9607, México.  相似文献   

10.
Let be a 1-convex holomorphic mapping between complex spaces resp.S, and let be the blowingdown factorization of over S. We prove in part 1 of the present note: The fiber –1(s0) over a point s0S is the Remmert quotient of if and only if every holomorphic function on (defined in a neighborhood of the exceptional subvariety of that fiber) can be extended holomorphically to . This is true, for instance, in the case: flat, S reduced at s0 and dim , =const for all sS. In part 2, we use this result to obtain the following: For any Riemann surface R with genus g2 there exists a 2-dimensional normal complex analytic singularity X such that the minimal resolution of X contains R as exceptional subvariety, and has a deformation over the unit disc S={|s|<1} which can not be blown down to a deformation of X.  相似文献   

11.
Let be a semisimple Lie algebra overk, an algebraically closed field of characteristic zero, and let be a Cartan subalgebra inside a Borel subalgebra of . LetU be the enveloping algebra of . For letM() denote the corresponding Verma modúle and letU u=U/AnnM(). LetW be the Weyl group and letW 0 be the stabiliser of inW. We prove the following theorem, which affirms a conjecture of T.J. Hodges.Oblatum 16-XII-1994  相似文献   

12.
Summary We study the Hellinger type distances on a filtered space. Herep2 is an arbitrary number andP T and are two probability measures stopped at a random timeT. We give lower and upper bounds for in predictable terms.  相似文献   

13.
We consider the on-line computation of the lattice of maximal antichains of a finite poset . This on-line computation satisfies what we call the linear extension hypothesis: the new incoming vertex is always maximal in the current subposet of . In addition to its theoretical interest, this abstraction of the lattice of antichains of a poset has structural properties which give it interesting practical behavior. In particular, the lattice of maximal antichains may be useful for testing distributed computations, for which purpose the lattice of antichains is already widely used. Our on-line algorithm has a run time complexity of , where |P| is the number of elements of the poset, , |MA(P)| is the number of maximal antichains of and (P) is the width of . This is more efficient than the best off-line algorithms known so far.  相似文献   

14.
Two functionals (A) and for an operatorA were introduced in [11] for the study of causality in commutant lifting theory. In this paper we give sufficient and necessary conditions for in a special case. We prove that in this case , and we show by some examples related to nonlinear system control that is the best constant in our inequality.  相似文献   

15.
Let be a nest in a separably acting factor . We present conditions for a factor to be a bimodule of the nest subalgebraalgß in which is singly generated in the norm topology. Some relevant results about the compact ideal , the quasitriangular algebra and the Calkin algebra are established.This work was supported, in part, by funds provided by the University of North Carolina at Charlotte.  相似文献   

16.
A linear operatorT L(H) is called a strongly irreducible, if there is no non-trivial idempotent linear operator commuting withT. In this paper, denote the set of all strongly irreducible operators by (SI). Let be a nest with infinite dimensional atoms, be the nest algebra associated with and be the closure of , then the following result is proved
.The projection partially supported by Chinese Natural Science Foundation and Fund of Laboratory of Nonlinear Mathematical Modeling and Methods in Fudan University in Shanghai P.R.C.  相似文献   

17.
Given a sequence of independent, but not necessarily identically distributed random variables,Y i , letS k denote thekth partial sum. Define a function by taking to be the piecewise linear interpolant of the points (k, S k ), evaluated att, whereS 0=0, andk=0, 1, 2,... Fort[0, 1], let . The are called trajectories. With regularity and moment conditions on theY i , a large deviation principle is proved for the .  相似文献   

18.
Let CP (R) be the group of compactly supported homeomorphisms ofR= which are piecewise with a parabolic defect at each breakpoint. An acyclic extension
  相似文献   

19.
It is known [KRS] that for each finitely generated Banach algebra there exists a numberN such that for eachn>N the matrix algebras can be generated by three idempotents. In this paper we show that the same statement is true for direct sums and , where is a finitely generated free algebra, i.e. polynomials in several non-commuting variables. These results are new even for algebras because the numberN we obtain here improves known estimates (see for example [R]). We show that the algebra can be generated by two idempotents if and only ifn j =2 for eachj and is singly generated. Also we give an example of a free singly generated algebra for which can not be generated by two idempotents. But% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgznf% gDOfdaryqr1ngBPrginfgDObYtUvgaiuaacuWFSeIqgaacaaaa!409A!\[{\tilde {\cal B}}\] can be generated by three idempotents for each singly generated free algebra .  相似文献   

20.
Let and the foliations by the null geodesics of some lorentzian metricg on the torus . We analyse how geodesic completeness properties ofg are related to the dynamics of and .  相似文献   

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